Rarely has a party’s profile reversed itself with such striking swiftness. Less than two years ago, the Republican Party was flying high. The 2014 congressional elections had given the GOP its largest House majority in 86 years and the largest midterm gains any party had won in the Senate in more than a half-century. With more than a dozen young and appealing candidates contemplating presidential campaigns, the party seemed poised for glory.

The Republican rout was nationwide. They controlled two-thirds of the governors’ chairs and accounted for more than 55 percent of both state senators and state House members. Of the 30 states where one party controlled both houses of the legislature and the governor’s office, 25 of them were in Republicans hands. And while a new generation of Hispanic candidates and Spanish-speaking leaders seemed to answer the party’s demographic challenges, historical trends played to the GOP’s advantage — particularly Americans’ inclination for rotation in office. A typical post-election headline read “The Democrats’ lost generation.”

Yet with all that success and promise, today the Republican Party is headed by a Manhattan billionaire who rampaged through the 2016 primaries and caucuses, drawing new voters — wearing blue collars mostly — into the party even as he divided, belittled, and eventually demolished the GOP establishment, leaving the party in tatters and struggling to define its identity. As a result, Republicans across the country — activists, theorists, elected officials, party leaders — are beginning to confront a difficult question:

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What will be the shape of the Republican Party in the post-Donald J. Trump era?

The question has vital implications. For all its faults, our two-party system requires two strong parties, one in power and the other in opposition, with the loyal opposition committed to the business of governing even if it is shut out of the White House, Congress — or both. Political parties require self-confidence and a strong sense of identity — and these are the elements that the post-Trump GOP must win.

Even before the ballots are counted Nov. 8, the party is engaged in examining its post-Trump future, even as it is undertaking one of the most remarkable, dangerous, but potentially powerful transformations in American history. Today’s Republicans are on the verge of forging a new identity that obliterates more than a century of the party’s heritage and recasting it as a populist alternative to an increasingly elite Democratic Party. Or they’re on the precipice of destroying an important American institution that for four decades has been a force for austerity, social and cultural restraint, and traditional values.

“This presidential election is a big challenge,’’ said former Republican national chairman James Nicholson, who says he will vote for Trump. “We picked a very unconventional candidate. He’s not well known within the party, he doesn’t know a lot of people in the party — and he’s running a campaign that is not functioning very well.’’

No party has faced a choice or a challenge this daunting since 1928, when the Democrats, a largely conservative party of small farmers, Southerners, and easy-money populists, challenged the Republicans’ hold on its identity as the party of industrialization. Under Al Smith and then Franklin Delano Roosevelt, they emerged as the party of the poor and striving, workers, unions, blacks, ethnic Americans, Catholics, and Jews.

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“If Trump wins, the Republican Party will be fundamentally changed,’’ says Walter J. Stone, a political scientist at the University of California Davis. “But even if he loses, there’s the Trump constituency that has been activated. Trump’s candidacy has brought to the fore a set of issues the Republican Party has not dealt with and will have to deal with.’’

Those issues are manifold. Is the Republican Party after Trump the free-trade party it was throughout the second-half of the 20th century or the protectionist party it was at the end of the 19th century? Is it committed to building democratic institutions and regimes abroad or is it a party that, as Trump vowed in his Youngstown, Ohio, speech on terrorism, will bring a “swift and decisive end’’ to nation-building? Is it the interventionist party it was during the Cold War, when vocal elements of the Republican Party spoke of “liberating’’ the “captive nations’’ behind the Iron Curtain, or is it the isolationist party where Mr. Trump speaks of withdrawing US forces from forward positions around the globe?

Is the post-Trump GOP the party of Main Street, as it was in the early 1920s, or the party of Wall Street, as it was labeled at the end of that raucous decade? Are the Republicans after Trump’s 2016 campaign the party of black liberation, as in the Abraham Lincoln years, or are they the party of white backlash, as in the Richard Nixon years? Does the Republican Party after Trump favor federal regulation, as it did in the years of Theodore Roosevelt and William Howard Taft, or does the party, whose 2016 leader called for “a temporary moratorium on new agency regulations’’ only two weeks ago, favor laissez-faire business practices, as it did in the Ronald Reagan years?

But most of all — more important than what Trump says on the stump in the next several weeks, more important than whether he wins — is whether the new voters Trump has corralled into his constituency remain Republicans, whether they help transform the GOP identity, and whether those new Republicans and that new identity fundamentally alter the physics of politics.

“All those blue-collar folks might hang around,’’ said former governor William F. Weld, a prominent Northeastern Republican now running as the vice-presidential candidate on the Libertarian Party ticket. “Trump himself has said he sees a different Republican Party in five or 10 years. I don’t think they go back to the Democratic Party. The Democrats are getting too fancy for them.’’

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That possibility has vital implications for the Republicans’ rivals. For three generations many Trump supporters and their families have had a comfortable home within the Democratic Party, which since Al Smith and FDR has been the repository of the aspirations of blue-collar Americans and the idealistic visions of those who were determined, in a phrase from Tennyson appropriated by Senator Robert F. Kennedy, to “seek a newer world.’’

For all its faults, the American two-party system requires two strong parties, one in power and the other in opposition.

But the implications go far beyond a single party or candidate. If the post-Trump Republicans retain those blue-collar voters and ingest their aspirations, the normal rhythms of politics will be altered, the customary assumptions that animate life on Capitol Hill will be overhauled, and the very dynamics of American politics will be transformed.

The political geography is already changing. Republicans now face headwinds in Utah and Idaho, states they’ve won with ease in every election since 1952, with the exception of the 1964 Lyndon Johnson landslide over Senator Barry Goldwater. Last month, Hillary Clinton campaigned in deep-red Nebraska, and polls show toss-ups in Georgia and Goldwater’s home state of Arizona.

At the center of all these questions are the character and inclinations of a tradition-shattering nominee, a man who ran against the Republican Party to win its nomination; who suggested that the party process that he mastered was rigged and corrupt; who has embraced (and helped fund) some Democratic nostrums and many of its top figures, including both Bill and Hillary Clinton, in the past; and who has alienated the party leadership, including by several accounts party chairman Reince Priebus, and many of its members even as he has attracted millions to the party’s autumn White House fight.

“If he wins, he will have the executive branch, be able to appoint Cabinet positions, and have a lot of patronage, putting him in a very strong position,’’ said Kenneth L. Khachigian, an aide to both Nixon and Reagan. “The question is whether he is interested in being a party leader and building the party.’’

Polls this month show Trump lagging in his race with Hillary Clinton, with some prognosticators suggesting that the likelihood of a Clinton triumph is well over 85 percent. But Trump has been down before — and recovered quite easily against opponents who did not remotely have Clinton’s stubborn, soaring negative ratings. And no political strategist or commentator forgets the 1988 presidential race, when, in a midsummer poll by the Gallup Organization, Governor Michael Dukakis led Vice President George H.W. Bush by 17 percentage points. Bush won the election by nearly 8 points, with an electoral vote margin of nearly four-to-one.

Even so, according to Richard Norton Smith, a biographer of three formidable 20th century Republicans — Thomas E. Dewey, Nelson A. Rockefeller, and Gerald R. Ford — “you could imagine a scenario quite easily where Trump loses by 10 percent and the immediate reaction is that the party didn’t nominate an authentic conservative.’’

That already is a major theme in GOP circles, where Trump’s lack of conservative bona fides rankles a group that thought it was in the ascendancy, particularly after Tea Party conservatives flourished in recent elections, ousted House Speaker John Boehner of Ohio, and provided the balance of power in the struggle to succeed him. New Speaker Paul Ryan of Wisconsin is as devoutly conservative as former speaker Thomas P. O’Neill of Cambridge was devoutly liberal.

Conservatives have been reluctant warriors in the 2016 campaign, and many of them have been conscientious objectors. Some, such as Senator Ted Cruz of Texas, whose failure to endorse Trump became a cause celebre at the GOP convention in Cleveland, are keeping their distance. Others, including the editorial page of The Wall Street Journal, express skepticism and, on occasion, outrage. Still another group — former GOP nominee Robert J. Dole, for example, who was viewed warily by conservatives during his days as Senate majority leader — has sided with Trump. But others are expressing their contempt for those who endorse him.

“Conservatives are already tailoring their morality, decency, and political sense to fit Trumpism,’’ Ben Shapiro wrote earlier this month in The National Review, the journal founded by William F. Buckley Jr., and one flagship of the self-described #NeverTrump faction of the conservative movement. “We’ve already seen supposed conservative ‘thought leaders’ go silent when Trump does something unthinkable; we’ve already seen Chris ‘Shinebox’ Christie and Reince ‘The Enforcer’ Priebus and Newt ‘Dude, Who Stole My VP Slot?’ Gingrich embrace the Trump-or-bust logic that puts conservatism under the wheels of the Trump Train.’’

Party schisms are common — Democrats fought over civil rights in the early 1960s and over Vietnam in the late 1960s. Republicans battled for the entire second half of the 1970s over whether to stick with their traditional support for budget austerity or to accept supply-side economics.

Indeed, in the last two-thirds of a century, Republicans have split along several fault lines: Robert Taft conservatives and Dwight Eisenhower regulars in the beginning of the 1950s; Nixonites and Northeastern Republicans in 1960; moderate Republicans and the conservative intellectual vanguard that supported Goldwater in 1964; religious conservatives and economic conservatives at the end of the 1980s and into the 1990s; and new conservatives and the neoconservatives in the George W. Bush years.

“The transformation of the Republican Party has been coming for a long time, and the populist shift in the party is the face of it,’’ said Greg Mueller, the communications director of the 1992 campaign of Patrick J. Buchanan, itself a party rebellion directed against President George H. W. Bush. “Plus there was a void in the Republican Party that Trump — a marketing genius — filled. This movement within the party is a lot bigger than the Republican establishment thinks it is, and it’s not going away.’’

Mueller believes that Trump could be creating a “much bigger and broader party’’ than most Republicans envision today. But along with the potential of a fresh GOP attuned to the concerns of struggling middle-class families, there is also potential for a party that is so divided that it has no coherent ideology or identity. Such an opposition party would have trouble both checking a Clinton presidency and advocating for those new voters it attracted.

“The Republican Party is like an animal with no head right now, just flailing around with no direction,’’ said Kathleen P. Iannello, a Gettysburg College political scientist. “If it is to survive in any shape or form, it is going to have a post-Trump strategy.’’

That is the peculiar situation for the Republicans. They didn’t contemplate a post-Nixon strategy in either 1960, when he lost, or in 1968, when he won — though the wreckage that Nixon left behind when he resigned in Watergate disgrace in 1974 might have been ameliorated had they done so. Nor did they contemplate a post-Reagan future in 1980 (perhaps not daring to think he would foster a new flowering of conservatism) nor a post-Bush future during the older Bush’s campaign in 1988.

Today, there is contemplation of the existential variety. Former president George W. Bush recently told some of his former aides that he was worried “that I will be the last Republican president.” Now, does that mean that winning the White House is an unattainable goal for anyone from the GOP or that the party which Trump now helms isn’t Republican? The scion of the GOP dynasty didn’t say.

Yes, this time seems different.

At his worst, Trump projects the profile of a latter-day Huey Long, of whom his longtime critic J.Y. Saunders, a governor, said, “When it comes to arousing prejudice and passion, when it comes to ranting and raving, when it comes to vituperation and vilification, when it comes to denunciation and demagoguery, there is one who stands out by himself alone.” At his best, Trump projects the profile much like that employed by election chronicler Theodore S. White to describe Goldwater: “a patriot with an incandescent sense of mission’’ whose “inner convictions tell him that America is in danger.’’ And Trump has had a wider appeal than Goldwater did in the primaries and spoke about broadening the Republican electorate, a sharp contrast with the Goldwater forces, who were more intent on purity than on politics.

Whether Trump wins and gives the Republicans control of two of the three branches of the federal government or is defeated in a landslide repudiation, the issues he is raising in 2016, and the constituency he amassed in the primaries and caucuses, will prompt a substantial period of GOP soul-searching.

If Trump prevails, he will not necessarily face easy sailing in Washington. Outsider presidents, as the Jimmy Carter experience reminds us, may believe they have mandates but mostly they have minefields. One set of obstacles will be Republican leaders who embraced him warily, mostly out of obligation, or whose silence suggested serious reservations, or outright opposition, to his candidacy for the White House.

Then there are conservatives who want to cut the presidency down to size, no matter who wins. “Competent parties are not led by presidents but by congresses,’’ argued Grover Norquist, the conservative activist whose Americans for Tax Reform group has promulgated a widely signed pledge against new taxes. “The modern Republican Party has to learn how to govern through and from Congress. It almost doesn’t matter who the nominee is, and it almost doesn’t matter who is president, because the president is at the table but not the boss.

“If Trump gets elected,’’ he continued, “we don’t say, ‘This is the new rule because we don’t like you.’ It’s the rule because it’s the rule.’’

More than the Democrats, the Republicans remain split as the traditional Labor Day start to the campaign approaches. Among likely voters aged 19 to 29, according to a study by Harvard’s Institute of Politics at the Kennedy School of Government, Clinton is supported by about the same rate as a “generic Democrat’’ would receive — but Trump receives support levels 8 percentage points lower than a “generic Republican’’ would receive.

Among all demographic groups, only two-thirds of Republicans view Trump favorably, according to a Gallup Organization poll taken last week. Former governor Mitt Romney won the vote of 93 percent of Republicans, according to the Roper Center for Public Opinion Research at Cornell University. Trump is in danger of a far less formidable performance among his fellow party members; an astonishing 59 percent of Republicans disapproved of the way their nominee handled the Khans, the Muslim family who lost a son in combat, according to the Washington Post/ABC News Poll.

“Many Republicans believe some of the Trump remarks don’t reflect their fundamental human values,’’ said L. Sandy Maisel, a political scientist at Colby College. “When he speaks for Republicans, he makes statements they think reflect badly on them. The result is that there are tensions in the Republican Party that didn’t exist before.’’

Some of them come out of the new constituencies; some from the difficult choices of the 2008 economic recession; some from the combative style of the new nominee, who offers both promise and pause for reflection to a party hungry to return to the White House after more than seven years that have included an overhaul of health care, a nuclear treaty with Iran, terrorist incidents at home and abroad, and continued turmoil from North Africa to Pakistan.

“Good people in our party — Jeb Bush, George Pataki, John Kasich, Ted Cruz, all very different — have been cast aside by a nominee who is used to saying almost anything that comes into his head,’’ said Alexander T. Tennant of Swampscott, a former executive director of the state Republican Party and now a Trump supporter.

So the election features two deeply flawed and historically unpopular candidates.

“I don’t know how either party ends up after this because I can’t see people having respect for either of the candidates after this election,’’ said Paul H. O’Neill, who was secretary of the Treasury in the George W. Bush administration. “But this may be more acute for the Republicans. Their candidate has drifted from Republican Party orthodoxy, so much so that with Trump out there I don’t think there is any Republican Party anymore.’’

Forgotten — or nearly so — in all of this is the purpose of a political party, an institution that was not contemplated in the Constitution but that has served the United States well, presenting presidential candidates, applying discipline to politics, and serving as an instrument that brings order and clarity to political debate.

In “The Life of the Parties,’’ his classic 1992 history of American political parties, A. James Reichley argued that “the basic strength of successful parties in times past, as many of the technicians and bosses themselves would concede, lay not in machinery or techniques or systems of organization, but in the sense of public purpose that moved their grassroots workers and the voters who identified with them in the electorate.’’

Living up to that high-minded standard is the challenge both parties face after every election, but one that is especially challenging for the Republicans this time. For amid the formidable support that Trump has built, there is a foundation of party unease, unmatched this century.

“Trump has left a lot of damage,’’ says John J. Pinckney Jr., a political scientist at Claremont McKenna College in California. “How much of it heals, how much gets cleaned up, remains to be seen. But there’s no question he’s burned down a large part of the Republican house.”

David M. Shribman, a former Globe Washington bureau chief, is executive editor of the Pittsburgh Post-Gazette.